JuliaManifolds · kellertuer · Mar 6, 2025 · Mar 1, 2025 · Mar 1, 2025 · Mar 2, 2025
diff --git a/NEWS.md b/NEWS.md
@@ -5,7 +5,7 @@ All notable Changes to the Julia package `LieGroups.jl` will be documented in th
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [0.1.0] – unreleased
+## [0.1.0] unreleased
 
 Everything denoted by “formerly” refers to the previous name in [`Manifolds.jl`](https://juliamanifolds.github.io/Manifolds.jl/stable/).
 

diff --git a/docs/CondaPkg.toml b/docs/CondaPkg.toml
@@ -0,0 +1,3 @@
+[deps]
+jupyter = ""
+python = "3.11"
diff --git a/docs/make.jl b/docs/make.jl
@@ -93,6 +93,9 @@ if run_quarto || run_on_CI
         run(`quarto render $(tutorials_folder)`)
         return nothing
     end
+else
+    # fallback to at least create empty files for tutorials that are directly linked from the docs
+    touch(joinpath(@__DIR__, "src/tutorials/getstarted.md"))
 end
 
 # (d) load necessary packages for the docs

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -8,4 +8,47 @@ CurrentModule = LieGroups
 
 ```@docs
 LieGroups.LieGroups
-```
+```
+
+The implemented [Lie groups](https://en.wikipedia.org/wiki/Lie_group) are implemented using the interface for manifolds in [`ManifoldsBase.jl`](@extref ManifoldsBase :doc:`index`) together with additional interfaces [for Lie groups](interface/group.md) and [Lie algebras](interface/algebra.md) as well as internally using the manifolds implemented in [`Manifolds.jl`](@extref Manifolds :doc:`index`).
+
+For more general information about the history of and contributions to the package see the [About](about.md) page.
+
+## Getting started
+
+To install the package just type
+
+```julia
+using Pkg; Pkg.add("LieGroups")
+```
+
+Then you can directly start, for example consider the [`SpecialEuclideanGroup`](@ref)
+``\mathrm{SE}(3)`` representing all orientations and places an object can take in ``ℝ^3``.
+These are characterised by a ``3×3`` rotation matrix together with a point the object is at.
+For example.
+having such a point, we can use the Lie group logarithmic function [`log(G::SpecialEuclideanGroup, g)`](@ref)
+and the Lie group exponential function [`exp(G::SpecialEuclideanGroup, X)`](@ref)
+to create an orientation “half the way” from the origin pose.
+
+The default representation is in [homogeneous coordinates]()
+
+```@example start
+using LieGroups
+SE3 = SpecialEuclideanGroup(3)
+g = 1/sqrt(2) .* [1.0 -1.0 0.0 0.0; 1.0 1.0 0.0 3.0*sqrt(2); 0.0 0.0 sqrt(2) 0.0; 0.0 0.0 0.0 sqrt(2)]
+```
+
+Then half that pose is
+
+```@example start
+h = exp(SE3, 0.5 .* log(SE3, g))
+```
+
+To check, just “perform that movement” twice with the group operation
+[`compose`](@ref) of `h` with itself to get `g` back
+
+```@example start
+compose(SE3, h, h)
+```
+
+for more details see the [get started](tutorials/getstarted.md) tutorial.
diff --git a/docs/src/references.bib b/docs/src/references.bib
@@ -2,6 +2,7 @@
 #
 #
 # A
+# ------------------------------------------------------------------------------------------
 @article{AndricaRohan:2013,
     AUTHOR  = {Andrica, D. and Rohan, R.-A.},
     ISSUE   = {2},
@@ -28,9 +29,7 @@ @book{BinzPods:2008
 #
 #
 # G
-#
-# G
-# ----------------------------------------------------------------------------------------
+# ------------------------------------------------------------------------------------------
 @article{GallierXu:2002,
     AUTHOR  = {Gallier, J and Xu, D},
     ISSUE   = {4},
@@ -58,6 +57,7 @@ @inproceedings{Giles:2008
 #
 #
 # H
+# ------------------------------------------------------------------------------------------
 @book{HilgertNeeb:2012,
     AUTHOR    = {Hilgert, Joachim and Neeb, Karl-Hermann},
     DOI       = {10.1007/978-0-387-84794-8},
@@ -67,6 +67,22 @@ @book{HilgertNeeb:2012
     YEAR      = {2012}
 }
 
+#
+#
+# L
+# ------------------------------------------------------------------------------------------
+@article{LatifiToomanian:2013,
+    AUTHOR  = {Latifi, Dariush and Toomanian, Megerdich},
+    DOI     = {10.1186/2251-7456-7-37},
+    ISSN    = {2251-7456},
+    JOURNAL = {Mathematical Sciences},
+    MONTH   = aug,
+    NUMBER  = {1},
+    PAGES   = {37},
+    TITLE   = {On the existence of bi-invariant {Finsler} metrics on {Lie} groups},
+    VOLUME  = {7},
+    YEAR    = {2013}
+}
 #
 #
 # S

diff --git a/docs/src/tutorials/transition.md b/docs/src/tutorials/transition.md
@@ -31,7 +31,7 @@ The list is alphabetical, but first lists types, then functions
 | `SemidirectProductGroup(G, H, a)` | [`LeftSemidirectProductLieGroup`](@ref)`(G, H, a)` | While this staid the same, there is now also the [`default_left_action`](@ref)`(G,H)`. When this agrees with `a` you can use the short hand `G⋉H` to generate this semidirect product. Analogously there now also exists the [`RightSemidirectProductLieGroup`](@ref)`(G,H)` with[`default_left_action`](@ref)`(G,H)` that allows for the short cut `G⋊H` |
 | `RightBackwardAction` | [`RightGroupOperationAction`](@ref) | |
 | `RightForwardAction` | [`InverseLeftGroupOperationAction`](@ref) | note that this is an [`AbstractRightGroupActionType`](@ref) |
-| `adjoint` | [`adjoint`](@ref) | now implemented with a default, when you provide [`diff_conjugate!`](@ref).
+| `adjoint_action` | [`adjoint`](@ref) | now implemented with a default, when you provide [`diff_conjugate!`](@ref).
 | `apply_diff` | [`diff_apply`](@ref) | modifiers (diff) come first, consistent with [`ManifoldsDiff.jl`](https://juliamanifolds.github.io/ManifoldDiff.jl/stable/) |
 | `apply_diff_group` | [`diff_group_apply`](@ref) | modifiers (diff/group) come first, consistent with [`ManifoldsDiff.jl`](https://juliamanifolds.github.io/ManifoldDiff.jl/stable/) |
 | | [`conjugate`](@ref), [`diff_conjugate`](@ref) | a new function to model ``c_g: \mathcal G → \mathcal G`` given by ``c_g(h) = g∘h∘g^{-1}`` |

diff --git a/src/interface.jl b/src/interface.jl
@@ -394,7 +394,7 @@ _doc_exponential = """
     exp(G::AbstractLieGroup, X::T)
     exp!(G::AbstractLieGroup, g, X)
 
-    Compute the (Lie group) exponential function
+Compute the (Lie group) exponential function
 
 ```math
 $(_tex(:exp))_{$(_math(:G))}: $(_math(:𝔤)) → $(_math(:G)),$(_tex(:qquad)) $(_tex(:exp))_{$(_math(:G))}(X) = γ_X(1),

diff --git a/tutorials/Project.toml b/tutorials/Project.toml
@@ -1,3 +1,13 @@
 [deps]
 IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
 LieGroups = "6774de46-80ba-43f8-ba42-e41071ccfc5f"
+Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+Rotations = "6038ab10-8711-5258-84ad-4b1120ba62dc"
+
+[compat]
+IJulia = "1.26"
+LieGroups = "0.0.3"
+Manifolds = "0.10.14"
+RecursiveArrayTools = "3.31"
+Rotations = "1.7"